If a and b are integers such that a - b = 100, find the minimum value of a*b.
+678 "deleted" realized my answer is wrong
+738 if negatives are fine, then its -2500
if it's only positive answers, then I'm pretty sure its 101
+310 The closer two numbers with the same sum are, the bigger their product.
In this case, the problem did not specify whether positive or negative so the minimum value is: 50-(-50)=100
Therefore, a*b= -2500
+9519 Because \((a,b )\in \mathbb Z^2\), it is optimal to minimize b and maximize a.
Because of that reason, if we choose (a, b) = (50, -50), then we get our minimum value, which is -2500.
(If a was larger, then b would be smaller. Same otherwise. It is actually optimal to choose |a| = |b|, or make |a| as close as |b|.)
